Every time Apple releases a new iPhone, there's always the question of whether or not your old case will work with the new models. Thankfully, Apple's own store suggests older cases will still work.
If you take a look at one of Apple's iPhone 6s leather cases, you'll find this little note:
The case fits snugly and your iPhone 6s or iPhone 6 still feels incredibly slim, even with the case on.
Which is all to say that despite the the chunkier phone, old cases should work (tighter cases could have problems). So don't rush out and spend a ton of money on a specific 6s/6s Plus case unless you want to.